Rapid prototyping is used to construct physical objects, particularly prototype parts or small volume manufactured components. Rapid prototyping systems make use of additive manufacturing technology, wherein a machine uses digital data from a virtual model of the object and deposits successive layers or parcels of liquid, powder, or sheet material, corresponding to layers or parcels of the virtual model. The layers or parcels bind together (either upon contact or by application of heat and/or binding materials), and the part is thereby produced.
To date, there have been no commercial 3D printers capable of rapid manufacture of realistic-looking, aesthetic teeth, veneers, or other dental implants. This largely has to do with the variation in color, translucency, hardness, and other properties within a tooth, and the difficult of manufacturing a close replica of such a complex organic object.
The optical properties of a solid material are defined by the way in which light waves interact with it through absorption, scattering, reflection, transmittance and refraction. When white light is incident on a solid material, its color is defined by which frequencies are absorbed, and which are reflected back (or transmitted, in the case of glass) to an observer. The reflection can be either reflective, in which case the object will have a specular or glossy appearance, or diffusive, in which the object will appear to have a more matte finish.
Tooth enamel, dentin, cementum, and dental pulp are four major tissues which make up the tooth in vertebrates. Enamel is the hardest and most highly mineralized substance in the human body. Enamel is the visible dental tissue of a tooth because it covers the anatomical crown and is supported by the underlying dentin. Ninety-six percent of enamel is mineral, with water and organic material composing the rest. In humans, enamel varies in thickness over the surface of the tooth, often thickest at the cusp, up to 2.5 mm, and thinnest at its border with the cementum at the cementoenamel junction (CEJ). The normal color of enamel varies from light yellow to grayish white. At the edges of teeth where there is no dentin underlying the enamel, the color sometimes has a slightly blue tone. Since enamel is semi-translucent, the color of dentin and any material underneath the enamel strongly affects the appearance of a tooth.
Enamel's primary mineral is hydroxylapatite, which is a crystalline calcium phosphate. The large amount of minerals in enamel accounts not only for its strength but also for its brittleness. Tooth enamel ranks 5 on Mohs hardness scale and a Young's modulus of 83 GPa. Dentin, less mineralized and less brittle, 3-4 in hardness, compensates for enamel and is necessary as a support. On X-rays, the differences in the mineralization of different portions of the tooth and surrounding periodontium can be noted; enamel appears more radiopaque (or lighter) than either dentin or pulp since it is denser than both, both of which appear more radiolucent (or darker).
Enamel does not contain collagen, as found in other hard tissues such as dentin and bone, but it does contain two unique classes of proteins—amelogenins and enamelins. While the role of these proteins is not fully understood, it is believed that they aid in the development of enamel by serving as a framework for minerals to form on, among other functions. Once it is mature, enamel is almost totally absent of the softer organic matter. Enamel is avascular and has no nerve supply within it and is not renewed, however, it is not a static tissue as it can undergo mineralization changes.
Optical transparency in polycrystalline materials is limited by the amount of light which is scattered by their microstructural features. Light scattering depends on the wavelength of the light. Limits to spatial scales of visibility (using white light) therefore arise, depending on the frequency of the light wave and the physical dimension of the scattering center. For example, since visible light has a wavelength scale on the order of a micrometer, scattering centers will have dimensions on a similar spatial scale. Primary scattering centers in polycrystalline materials include microstructural defects such as pores and grain boundaries.
The hardness of a solid material is determined by its microstructure, or the structure and arrangement of the atoms at the atomic level. At the atomic level, the atoms may be arranged in an orderly three-dimensional array called a crystal lattice. However, a given specimen of a material likely never contains a consistent single crystal lattice. The material will likely contain many grains, with each grain having a fairly consistent array pattern. At a smaller scale, each grain contains irregularities. It is these irregularities at the grain level of the microstructure that are responsible for the hardness of the material.
When considering the rapid manufacture of non-homogeneous articles, such as teeth, material parameters need to be precisely controlled throughout the print volume in order to achieve an aesthetically acceptable result, since those parameters vary throughout the volume of the object. For example, color, translucency, hardness, elasticity, and the like, vary throughout the solid.
Current prototyping techniques employ Stereo Lithography File (STL) data structures (e.g., triangles or other polygons defining the surface of the object) that rapid prototyping machines use as input. Even in the simplest case where only a single parameter, such as color, varies throughout a solid, the required STL-based geometry is difficult to construct. For example, consider a red and white candy cane. Using STL geometry would first require defining the surface of the basic cane, then defining the complicated spiral shape of the red surface independently; and then performing a constructive-solid-geometry operation to define the white surface through a subtraction.
There is a need for improved methods for rapid prototyping of non-homogenous objects.
Volumetric representations readily maintain a watertight model without holes or self-intersections. Such representations naturally support Boolean operations based on a voxel-by-voxel compositing process. A voxel is a volume element. In order to perform the methods of the invention, an initial model is created. This model comes from various sources including scans of physical objects or prior interactive editing. The voxel model, or an alternative initial model, is represented by numerical values maintained in computer memory in an array.